I have two 6-7 year old cats that have always lived in apartments. I'm about to move to a new apartment that as a balcony (on the fifth floor), which will be a new thing for them. Now, these are purely indoor cats, and not terribly bright. Should I restrict them from going on the balcony for fear that they will fall, or knock each other off?

The only thing I have to say is, the neighboring balcony owner has a cat that jumps from the top of the balcony to a closeby tree, and from there climbs to the ground. They don't even have to let it out. It also climbs back up the same way.

High rise syndrome is a veterinary term that describes cats that fall/are pushed from balconies. Fairly common scenario IME. Fractures of the mandibular symphysis are common.

Years ago PETA embarrased themselves by protesting an article in the vet literature about this syndrome. The paper was a retrospective study that detailed the outcomes of falls by height. PETA misinterpreted this to be a paper in which cats were dropped intentionally to gather data. Heh.

Definitely restrict their access. Cats like to chase birds, and they don't often look where they are going, in my experience.

I grew up in a house with cathedral ceilings and a balcony on the third floor across the living room. The cats took great delight in walking along the handrail, and they often fell. Now, they only fell 20 feet, so it was more "look at the stupid cat" (who was, by then, nonchalantly licking a paw in a "I meant to do that" way) than a "my cat just fell five stories" shock.